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2
votes
2answers
246 views

Algorithm to compute the intersection of meshlines with a boundary

I need a program or an algorithm that computes the intersection of a mesh and a boundary. The mesh is structured orthogonal in nature and the boundary is a circle (for example). This will be used ...
13
votes
5answers
533 views

How much should scientific software be optimized?

For applications requiring significant computational resources, high performance can be a critical factor when it comes to delivering scientific results or achieving "break-throughs" in reasonable ...
10
votes
3answers
3k views

How to construct a prolongation and restriction operator for an algebraic multigrid solver?

I am trying to solve a linear system of equations that is sparse, but lacks any kind of banded structure. I have heard that there is a way to extend the principles of a multigrid solver for implicit ...
11
votes
3answers
917 views

Which linear algebra texts should I read before learning numerical linear algebra?

Assuming one wishes to study numerical linear algebra in depth (and follow journals on numerical linear algebra and matrix theory), which would be a better course/better book to take up at first: ...
7
votes
1answer
864 views

Sparse hermitian eigensystems: are there better techniques than Arpack or TRLan?

As a part of other work I need to solve relatively large (~1E5x1E5) and sparse (~100 non-zero elements in each raw in few blocks) hermitian eigensystems. Usually only few eigenvalues+vectors are ...
8
votes
4answers
3k views

High Order derivatives of splines using SciPy

I have created a spline to fit my data in python using: spline=scipy.interpolate.UnivariateSpline(energy, fpp, k=4) The equation I want to use involves a ...
10
votes
2answers
801 views

Which journals should I read to keep up on advances in solving PDEs numerically?

I solve a lot of PDEs numerically, but applied math isn't my field. I haven't picked up on which applied math journals I should read to keep up with recent developments in the field. What are good ...
7
votes
2answers
359 views

Open-access journals in Computational Science

In light of the recent petition to boycott Elsevier, I was wondering what options we have in Computational Science for Journals which are completely open-access, Journals which allow/support open-...
7
votes
4answers
594 views

When analyzing a parallel algorithm, how do you take communication costs into account?

My question is related in spirit to "Is algorithmic analysis by flop counting obsolete?". Counting the number of computational operations in an algorithm is commonly used as a first-order model to ...
5
votes
2answers
356 views

Pauli repulsion contribution in electronic structure computations

I am looking for a method to estimate the contribution from Pauli repulsion to the interaction energy of a molecular dimer in an electronic structure computation (e.g. with Density Functional Theory). ...
2
votes
0answers
183 views

Texture analysis methods modern survey paper

I want to study the methods of analyzing textured images. So i searched google scholor but only found very old papers statistical and structural approaches to texture 1979 haralick Image Texture ...
5
votes
1answer
126 views

Using an approximation algorithm to adapt parameter values of a given algorithm

Problem: I have an incremental online clustering algorithm which need 4 parameters that should be specified by the user before execution. The algorithm will gives "good results" if "a good parameter ...
4
votes
2answers
172 views

What mapping strategy should I use when solving many large linear systems of equations?

I am working on a problem that involves solving many (thousands) of distinct linear systems of equations, each with thousands of variables. Let's assume that the size of each matrix is exactly the ...
4
votes
0answers
286 views

How does one handle the source term in the Shallow Water Equations when using the discontinuous galerkin method? [closed]

I use the discontinuous galerkin method to solve the steady flow 1D shallow water equations with a bump at the bottom. This flow is frictionless. I use the runge-kutta method to approximate the time ...
4
votes
1answer
681 views

Diffusion kernel “guide”

Diffusion kernels are kernels which "project" information about graphs into $R^n$ so that certain machine learning techniques can be performed. I have read through this paper and feel fairly ...
7
votes
1answer
174 views

Conjugate Gradient with Hierarchical Basis Functions: How can the hierarchical base be decomposed?

I'm trying to implement a Conjugate Gradient solver using Hierarchical Basis Functions, following this paper. In section 3 the paper says that the hierarchical basis matrix $S$ can be decomposed into ...
5
votes
2answers
484 views

Implementing a fair scheduling policy on Maui/Torque

We have Maui and Torque on our lab's UNIX cluster. Right now, all jobs are served by FIFO. We'd like to implement a more fair policy, but I have not successfully implemented it. The online ...
5
votes
5answers
12k views

How can I plot piece-wise defined function in some easily-accessed open-source tool?

I want to plot $$f_{n}(x) = \begin{cases} x-n & \text{for } n \leq x \leq n+1 \\ 2-x+n & \text{for } n+1\leq x \leq n+2 \\ 0 &...
7
votes
2answers
144 views

Can quantum methods be applied to the protein-ligand docking problem?

In the problem of protein-ligand docking, most of the time people are happy if they can just predict the final conformation the ligand adopts into the protein's binding pocket. Most of the time one ...
2
votes
1answer
197 views

Power series approximation for any function such as $-e^{x^{2}}$ in some easily-accessed open-source software?

My comrades repeatedly encourages monotonous problems where the issue is the same: chain-rule and some basic arithmetic. Is there some computational way to derive power series approximations? Suppose ...
8
votes
1answer
252 views

Adaptive mesh refinement with perfectly matched layers?

We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...
10
votes
3answers
837 views

Can I use an explicit time stepping scheme to determine numerically whether an ODE is stiff?

I have an ODE: $u'=-1000u+sin(t)$ $u(0)=-\frac{1}{1000001}$ I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (...
14
votes
2answers
2k views

How useful is PETSc for Dense Matrices?

Wherever I have seen, PETSc tutorial/documents etc. say that it is useful for linear algebra and usually specifies that sparse systems will benefit. What about dense matrices? I am concerned about ...
5
votes
1answer
312 views

Working with multi-dimensional functions

How would you represent functions of type $[-1, 1]^n \to \mathbb R \;$ for moderate $n$? How would you integrate them? For small $n$ (1-2) such functions can be represented as histograms, vectors in ...
17
votes
5answers
349 views

Databases of results for numerical codes

In the numerical methods literature, many research papers consist of a description of a new algorithmic variation, followed by a few test problems comparing the new method with one or two existing ...
7
votes
1answer
1k views

Alternative to Bron-Kerbosch algorithm for enumerating maximal cliques in inverse interval graphs

I often use inverse interval graphs to represent biologically relevant features along a genomic sequence. For example, given a (relatively) small genomic region, the graph would contain a node for ...
11
votes
1answer
1k views

How can I compute a basis for a matrix Lie algebra given a finite set of generators?

Given an arbitrary set of (numerical) square complex matrices $\mathcal{A}=\{A_1,A_2,\cdots,A_m\}$, I am interested in computing the real matrix Lie algebra generated by $\mathcal{A}$, call it $\...
17
votes
4answers
4k views

The definition of stiff ODE system

Consider an IVP for ODE system $y'=f(x,y)$, $y(x_0)=y_0$. Most commonly this problem is considered stiff when Jacobi matrix $\frac{\partial f}{\partial y}(x_0,y_0)$ has both eigenvalues with very ...
6
votes
2answers
319 views

What guidelines should I use when choosing a scalable linear solver?

There are many different linear solvers, some which work best for diagonally dominant matrices, some for symmetric, some for positive definite ones, some for banded matrices, etc... There are direct ...
3
votes
1answer
855 views

Is a checkerboard block decomposition of a matrix useful when solving a linear system with a parallel conjugate gradient method?

According to these lecture notes, a checkerboard block decomposition should exhibit better scalability when applied to parallel matrix-vector multiplication (presumably because of greater cache hit ...
6
votes
5answers
426 views

Where do dense matrices occur?

I have primarily dealt with Dense Matrices arising from Electrodynamics. However, I am interested in knowing where else Dense Matrices occur. I am especially interested in knowing where they occur in: ...
5
votes
3answers
760 views

Seemingly non-unique Cholesky factor via QR rectangularisation

I am trying to implement an algorithm from a paper which makes use a QR factorization of a real matrix $A$ as a means of one of forming the Cholesky factor of $A^T A$ without explicitly forming $A^T A$...
10
votes
3answers
1k views

Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...
5
votes
5answers
821 views

Introductions to hp-FEM

do you know good introductions into or surveys $hp$-adaptive finite elements? In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...
5
votes
2answers
1k views

Sufficient conditions to ensure convergence of the conjugate gradient method

I know that a conjugate gradient method is guaranteed to converge to the solution of a linear system if the matrix is positive definite. I'm working with a family of matrices that have the following ...
6
votes
2answers
1k views

Starting multiple processes from a single PBS job and distributing them on the free cluster nodes

I'm not very familiar with PBS (we have torque installed here), and I have only used it to run one process per job so far, so bear with me. The actual problem I am trying to use Mathematica on a ...
3
votes
1answer
280 views

How to solve a problem with structure similar to a finite difference discretization of the 2D Poisson equation, but with non-symetric coefficients?

Recently, I've been asking about methods to solve a finite difference discretization of the 2D Poisson equation (see here and here) of the form: $$U_{i-1,j} + U_{i+1,j} -4U_{i,j} + U_{i,j-1} + U_{i,...
5
votes
0answers
2k views

Two-chordless cycle extraction from a failed comparability graph recognition

I have implemented a comparability graph recognition algorithm from M.C. Golumbic's "Algorithmic graph theory and perfect graphs" book. It is hinted in Fekete, Schepers, and van der Veen's "Exact ...
2
votes
1answer
172 views

How can I set different axes for different plots in gnuplot?

I want to plot a few sets of data points on the same x-axis that have different units. How can I set different axes for each incompatible quantity?
8
votes
2answers
1k views

How do I compute the parallel overhead of a parallel code run on a single processor when no sequential code is available?

I'm profiling the performance of PETSc's linear solvers. As I understand it, $$\text{speedup}=\frac{\text{Sequential Time}}{\text{Parallel Time}}.$$ I know that running the parallel code on one ...
22
votes
4answers
3k views

When do orthogonal transformations outperform Gaussian elimination?

As we know, orthogonal transformations methods (Givens rotations and Housholder reflections) for systems of linear equations are more expensive than Gaussian elimination, but theoretically have nicer ...
18
votes
1answer
2k views

How can wavelets be applied to PDE?

I would like to learn how wavelet methods can be applied to PDE, but unfortunately I do not know a good resource to learn about this topic. It seems that many introductions to wavelets focus on ...
10
votes
2answers
3k views

What's the most efficient way to compute the eigenvector of a dense matrix corresponding to the eigenvalue of largest magnitude?

I have a dense real symmetric square matrix. The dimension is about 1000x1000. I need to compute the first principal component and wonder what the best algorithm to do this might be. It seems that ...
24
votes
5answers
6k views

What are the main differences between PETSc and Trilinos?

As far as I can tell, the two big generic US Department of Energy computational science software frameworks are PETSc and Trilinos. They seem similar at first glance, beyond differences in language (...
3
votes
1answer
197 views

Can BFGS be used to minimise several functions at once?

I have multiple objective functions which are related to several parameters. I want to minimise more than one objective functions using several parameters. Is it even possible using BFGS? When I used ...
2
votes
1answer
1k views

How to measure the overall performance of a PETSc program using the -log_summary flag?

When I run a PETSc example in parallel with the flag "-log_summary", the first two tables of information look something like this: ...
6
votes
4answers
279 views

Approximately “solving” a linear system of equations without a feasible solution

A linear system of equations has the form $Ax = b$, where a matrix $A$ and a vector $b$ are given, and I wish to find a solution vector $x$. Suppose that the system $Ax = b$ has no feasible solution. ...
15
votes
1answer
436 views

How effective is the 'tendrils of knowledge' approach to Comp. Sci?

I was reading this on Math SE. The basic question is : Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...
3
votes
1answer
1k views

Problems running a PETSc example in parallel

After configuring and building PETSc, I have successfully been able to run several examples. In particular, I am working with this example. I have been able to run the program using the following ...
7
votes
4answers
2k views

precision vs matrix condition number

I have an application in which I am computing a quantity which is approximated by an average over $M$ points. In theory, the average converges to the correct quantity when $M$ is infinite. In practice,...

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